Question

A worker is hired for $80 a day on the condition that if business is slow, the worker will only receive half pay.  At the end of 20 days, the worker receives $1,320.  On how many days was business slow?

Answer 1

7 slow days

You know the worker worked a total of 20 days, some at $80 per day, and some at $40 per day. After the 20 days, the worker was paid $1320.

x = days paid full time ($80)
y = days paid half time ($40)

you have two unknowns, so you'll need two equations to solve, from the problem statement, we can derive the following relationships:

($80)x + ($40)y = $1320
x + y = 20 days

x = 20 - y
80(20 - y) + 40y = 1320
1600 - 80y + 40y = 1320
1600 - 40y = 1320
1600 - 1320 = 40y
280 = 40y
y = 280/40 = 7

thus 7 days paid half time (i.e. slow days)

verify your solution is correct
y = 7
x = 20 - 7 = 13
80(13) + 40(7) = 1320 [OK]